An overview on the progeny of the skew-normal family— A personal perspective

Azzalini, Adelchi

doi:10.1016/j.jmva.2021.104851

Cited by 19 publications

(14 citation statements)

References 118 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…What is noteworthy about

t

‐skew distribution, apart from the ability to fit heavy‐tailed and skewed data, is “their mathematical tractability, the inclusion of the normal law as a proper member of the family, and the shape parameter regulating the skewness.” 3 Such an extension allows for a continuous variation from normality to non‐normality 10 . For an overview, see Azzalini 12 …”

Section: Literature Reviewmentioning

confidence: 99%

“…Furthermore, Maxwell and van Vuuren 20 build “TE‐constrained portfolios which are maximally diversified, exhibit risk parity, and have minimal intra‐correlation between constituents.” In this work, a key part of the optimization scheme is played by the ex‐ante tracking error which depends on distributions of asset returns. As mentioned, we will follow theoretical 8‐10,12,27 and empirical work 3 and, for the rest of the article, we will assume skewed return distributions.…”

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Forecasting portfolio returns with skew‐geometric Brownian motions

Bufalo

Liseo

Orlando

2022

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

The gist of this work is to propose a minimum tracking error portfolio that could be adopted not only as an automated alternative to ETFs but, it could also be potentially used to anticipate market changes in the target index. This goal has been achieved by adopting skew Brownian motion as a general framework.The proposed solution has been declined in two versions: the case in which the constituents (i.e., in our case the subindices) of the objective portfolio are uncorrelated among each other, and the case in which correlation should be taken into account. Our tests, carried out on the S&P 500, as an example of a developed market, and Bovespa, as an example of an emerging market, shows that the proposed solutions replicate the index with a much smaller tracking error than that of the ETFs considered.

show abstract

“…What is noteworthy about

t

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Forecasting portfolio returns with skew‐geometric Brownian motions

Bufalo

Liseo

Orlando

2022

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

show abstract

“…Azzalini and Capitanio (2003) followed by providing a general account of the t-skew class of densities by stressing their ability to fit heavy-tailed and skewed data. In particular, the inclusion of the normal law and the shape parameter regulating the skewness, allows for a continuous variation from normality to non-normality (see Azzalini, 2021). Recently, Bufalo et al (2022) described an application to forecasting portfolio returns with skew-geometric Brownian motions in presence of cross dependency between assets.…”

Section: On Skewed Distributions Of Returnsmentioning

confidence: 99%

“…In the following, we recall a standard definition of SABM process (see Atar and Budhiraja, 2015;Azzalini, 2021;Itô and Henry Jr, 1974).…”

Section: Skew Arithmetic and Geometric Brownian Motionmentioning

confidence: 99%

Straightening skewed markets with an index tracking optimizationless portfolio

Bufalo¹,

Bufalo²,

Cesarone³

et al. 2022

Preprint

View full text Add to dashboard Cite

Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent decades to offer returns close to benchmarks at a lower cost. In this article, we first refine the existing results on the theoretical properties of oblique Brownian motion. Then, assuming that the returns follow skew geometric Brownian motions and that they are correlated, we describe some statistical properties for the ex-post, the ex-ante tracking errors, and the forecasted tracking portfolio. To this end, we develop an innovative statistical methodology, based on a benchmark-asset principal component factorization, to determine a tracking portfolio that replicates the performance of a benchmark by investing in a subset of the investable universe. This strategy, named hybrid Principal Component Analysis (hPCA), is applied both on normal and skew distributions. In the case of skew-normal returns, we propose a framework for calibrating the model parameters, based on the maximum likelihood estimation method. For testing and validation, we compare four alternative models for index tracking. The first two are based on the hPCA when returns are assumed to be normal or skew-normal. The third model adopts a standard optimizationbased approach and the last one is used in the financial sector by some practitioners. For validation and testing, we present a thorough comparison of these strategies on real-world data, both in terms of performance and computational efficiency. A noticeable result is that, not only, the suggested lean PCA-based portfolio selection approach compares well versus cumbersome algorithms for optimization-based portfolios, but, also, it could provide a better service to the asset management industry.

show abstract

“…Depending on the application, the appropriate threshold or truncation point for Y might take any nonzero value, as might the value of the mean of its underlying normal distribution. For example, in his recent paper [3] refers to early work by [4]. The latter was concerned with the scores from admission examinations: in such a case, the mean of Y would surely be greater than zero, as would the truncation point.…”

Section: Introductionmentioning

confidence: 99%

Properties and Limiting Forms of the Multivariate Extended Skew-Normal and Skew-Student Distributions

Adcock

2022

Stats

View full text Add to dashboard Cite

This paper is concerned with the multivariate extended skew-normal [MESN] and multivariate extended skew-Student [MEST] distributions, that is, distributions in which the location parameters of the underlying truncated distributions are not zero. The extra parameter leads to greater variability in the moments and critical values, thus providing greater flexibility for empirical work. It is reported in this paper that various theoretical properties of the extended distributions, notably the limiting forms as the magnitude of the extension parameter, denoted t in this paper, increases without limit. In particular, it is shown that as t ! 􀀀¥, the limiting forms of the MESN and MEST distributions are different. The effect of the difference is exemplified by a study of stock market crashes. A second example is a short study of the extent to which the extended skew-normal distribution can be approximated by the skew-Student.

show abstract

An overview on the progeny of the skew-normal family— A personal perspective

Cited by 19 publications

References 118 publications

Forecasting portfolio returns with skew‐geometric Brownian motions

Forecasting portfolio returns with skew‐geometric Brownian motions

Straightening skewed markets with an index tracking optimizationless portfolio

Properties and Limiting Forms of the Multivariate Extended Skew-Normal and Skew-Student Distributions

Contact Info

Product

Resources

About